A projected conjugate gradient method for structural stability analysis with linear constraints
In this paper a new iterative method to solve an eigenvalue problem subject to linear homogeneous inequality constraints is presented. This approach allows study of the linearized equilibrium path stability of a structure submitted to unilateral contact conditions. The solution is obtained by using...
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| Published in | Computers & structures Vol. 33; no. 1; pp. 31 - 39 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Oxford
Elsevier Ltd
1989
Elsevier Science |
| Subjects | |
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| Abstract | In this paper a new iterative method to solve an eigenvalue problem subject to linear homogeneous inequality constraints is presented. This approach allows study of the linearized equilibrium path stability of a structure submitted to unilateral contact conditions. The solution is obtained by using a projected conjugate gradient technique to minimize the finite element discretized form of the Rayleigh quotient. The good behaviour of this algorithm is illustrated by some simple applications in structural mechanics. |
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| AbstractList | A new iterative method to solve an eigenvalue problem subject to linear homogeneous inequality constraints is presented. This approach allows study of the linearized equilibrium path stability of a structure submitted to unilateral contact conditions. The solution is obtained by using a projected conjugate gradient technique to minimize the finite element discretized form of the Rayleigh quotient. The good beheviour of this algorithm is illustrated by some simple applications in structural mechanics. In this paper a new iterative method to solve an eigenvalue problem subject to linear homogeneous inequality constraints is presented. This approach allows study of the linearized equilibrium path stability of a structure submitted to unilateral contact conditions. The solution is obtained by using a projected conjugate gradient technique to minimize the finite element discretized form of the Rayleigh quotient. The good behaviour of this algorithm is illustrated by some simple applications in structural mechanics. |
| Author | Sonzogni, Victorio Jeusette, Jean-Pierre |
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| Cites_doi | 10.1016/0022-460X(80)90520-9 10.1016/0020-7683(79)90081-7 10.1002/nme.1620211206 10.1016/0045-7949(81)90108-5 10.1016/0029-5493(84)90198-5 10.1016/0022-460X(71)90692-4 10.1093/comjnl/7.2.149 |
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| Keywords | Conjugate gradient method Finite element method Stability Inequality constraint Eigenvalue problem Mechanical structure Non linear effect Algorithm |
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| References | Papadrakakis, Yakoumidakis (BIB8) 1987; 62 Carnoy, Panosyan (BIB4) 1983 Riks (BIB2) 1979; 15 Bathe, Wilson (BIB14) 1976 Crisfield (BIB3) 1981; 13 Zoutendijk (BIB13) 1970 University of Liège, Liège. Timoshenko (BIB15) 1936 Carnoy, Panosyan (BIB1) 1984; 78 Bezine, Cimetière, Gilbert (BIB5) 1985; 21 Fleury (BIB9) 1978 Delsemme, Laschet (BIB6) 1986 Fletcher, Reeves (BIB10) 1964; 7 Papadrakakis (BIB11) 1980; 73 Géradin (BIB7) 1971; 19 Rosen (BIB12) 1960; 8 SAMCEF Fleury (10.1016/0045-7949(89)90126-0_BIB9) 1978 Riks (10.1016/0045-7949(89)90126-0_BIB2) 1979; 15 Papadrakakis (10.1016/0045-7949(89)90126-0_BIB11) 1980; 73 Carnoy (10.1016/0045-7949(89)90126-0_BIB1) 1984; 78 Crisfield (10.1016/0045-7949(89)90126-0_BIB3) 1981; 13 Papadrakakis (10.1016/0045-7949(89)90126-0_BIB8) 1987; 62 Rosen (10.1016/0045-7949(89)90126-0_BIB12) 1960; 8 10.1016/0045-7949(89)90126-0_BIB16 Carnoy (10.1016/0045-7949(89)90126-0_BIB4) 1983 Timoshenko (10.1016/0045-7949(89)90126-0_BIB15) 1936 Delsemme (10.1016/0045-7949(89)90126-0_BIB6) 1986 Géradin (10.1016/0045-7949(89)90126-0_BIB7) 1971; 19 Zoutendijk (10.1016/0045-7949(89)90126-0_BIB13) 1970 Bezine (10.1016/0045-7949(89)90126-0_BIB5) 1985; 21 Bathe (10.1016/0045-7949(89)90126-0_BIB14) 1976 Fletcher (10.1016/0045-7949(89)90126-0_BIB10) 1964; 7 |
| References_xml | – volume: 15 start-page: 524 year: 1979 end-page: 551 ident: BIB2 article-title: An incremental approach to the solution of snapping and buckling problems publication-title: Int. J. Solids Struct. – volume: 13 start-page: 55 year: 1981 end-page: 62 ident: BIB3 article-title: A fast incremental/iterative solution procedure that handles snap-through publication-title: Comput. Struct. – volume: 73 start-page: 353 year: 1980 end-page: 362 ident: BIB11 article-title: A numerical study of the solution of the partial eigenvalue problem publication-title: J. Sound Vibr. – volume: 8 start-page: 181 year: 1960 end-page: 217 ident: BIB12 article-title: The gradient projection method for nonlinear programming. Part I: linear constraints publication-title: SIAM J. – volume: 21 start-page: 2189 year: 1985 end-page: 2199 ident: BIB5 article-title: Unilateral buckling of thin elastic plates by the boundary integral equation method publication-title: Int. J. Numer. Meth. Engng – volume: 19 start-page: 319 year: 1971 end-page: 331 ident: BIB7 article-title: The computational efficiency of a new minimization algorithm for eigenvalue analysis publication-title: J. Sound Vibr. – volume: 62 start-page: 195 year: 1987 end-page: 207 ident: BIB8 article-title: A partial preconditioned conjugate gradient method for large eigenproblems publication-title: Comput. Meth. appl. Mech. Engng – year: 1978 ident: BIB9 article-title: Le dimensionnement automatique des structures élastiques publication-title: Ph.D. Thesis – reference: SAMCEF, – volume: 7 start-page: 149 year: 1964 end-page: 154 ident: BIB10 article-title: Function minimization by conjugate gradients publication-title: Comput. J. – reference: . 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Engng Des. doi: 10.1016/0029-5493(84)90198-5 – volume: 19 start-page: 319 year: 1971 ident: 10.1016/0045-7949(89)90126-0_BIB7 article-title: The computational efficiency of a new minimization algorithm for eigenvalue analysis publication-title: J. Sound Vibr. doi: 10.1016/0022-460X(71)90692-4 – volume: 62 start-page: 195 year: 1987 ident: 10.1016/0045-7949(89)90126-0_BIB8 article-title: A partial preconditioned conjugate gradient method for large eigenproblems – volume: 7 start-page: 149 year: 1964 ident: 10.1016/0045-7949(89)90126-0_BIB10 article-title: Function minimization by conjugate gradients publication-title: Comput. J. doi: 10.1093/comjnl/7.2.149 |
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| SubjectTerms | Buckling Exact sciences and technology Fundamental areas of phenomenology (including applications) Physics Solid mechanics Structural and continuum mechanics |
| Title | A projected conjugate gradient method for structural stability analysis with linear constraints |
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